Control of rheology of aqueous systems using water-soluble polymers is well-known. For instance, fully and partially hydrolyzed poly(vinyl acetate) have been used as thickeners in aqueous systems such as latex paints, and steric stabilizers and emulsion aids in suspension and emulsion polymerization. The thickening efficiency of fully and partially hydrolyzed poly(vinyl acetate) is quite low as compared to other water-soluble polymers, requiring higher molecular weight polymers to generate even a moderate thickening power. Therefore, there has been a need to improve the ability to control rheology using fully and partially hydrolyzed poly(vinyl acetate). According to this invention, this objective is achieved by grafting alkyl ketene dimer to fully and partially hydrolyzed poly(vinyl acetate). Other advantages of such polymers are described below.